Quantum Algorithms: Entanglement Enhanced Information Processing

Details Quantum Algorithms: Entanglement Enhanced Information Processing Quantum Algorithms: Entanglement Enhanced Information Processing

1998-03-26

arxiv.org/abs/quant-ph/9803072v1

Physics

Quantum Physics

17 pages latex, no figures. To appear in Phil. Trans. Roy. Soc. (Lond.) 1998, Proceedings of Royal Society Discussion Meeting

Scientific paper

10.1098/rsta.1998.0248

We discuss the fundamental role of entanglement as the essential nonclassical feature providing the computational speed-up in the known quantum algorithms. We review the construction of the Fourier transform on an Abelian group and the principles underlying the fast Fourier transform algorithm. We describe the implementation of the FFT algorithm for the group of integers modulo 2^n in the quantum context, showing how the group-theoretic formalism leads to the standard quantum network and identifying the property of entanglement that gives rise to the exponential speedup (compared to the classical FFT). Finally we outline the use of the Fourier transform in extracting periodicities, which underlies its utility in the known quantum algorithms.

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